Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No: 345.52007
Autor: Erdös, Paul; Purdy, George
Title: Some extremal problems in geometry. IV. (In English)
Source: Proc. 7th southeast. Conf. Comb., Graph Theory, Comput.; Baton Rouge 1976, 307-322 (1976).
Review: [For the entire collection see Zbl 328.00003.]
The authors discuss some questions and obtain new results on bounds for several functions occurring in problems of Combinatorial Geometry, mostly in the plane. Examples: Let f(n) denote the maximum number of times that unit distance can occur among n points in the plane if no three points lie on a line; then f(n) \geq 2n log n/6 /3 log 3. Let g(n) be the minimum number of triangles of different areas which must occur among n points in the plane, not all on a line; then c1n3/4 \leq g(n) \leq c2n. Let f(n) be the minimum number k such that there exist k points in the n by n lattice Ln so that the lines through any two of them cover all the points of Ln; then f(n) \geq cn2/3. Other similar problems are concerned with congruent triangles, isosceles triangles, congruent or incongruent subsets, always taken from n given points.
Reviewer: R.Schneider
Classif.: * 52A40 Geometric inequalities, etc. (convex geometry) 51M25 Length, area and volume (geometry) 00A07 Problem books